Table 1.
Sample Stream A 1% benzene 3% benzene 5Y0 benzene Stream B 15% ' toluene 20% toluene 25% toluene
Composition of Synthetic Calibration Samples
Benzene % Cc. 1 3 5
2.66 7.98 13.3 0 0 0
Toluene
cc.
70 40 40 40
129 129 129
1Yj
25
I n the event heavy ends are inadvertently allowed to pass and deposit on the cell windows, special valving has been provided to allow introduction of solvent to clean the windows. TEST RESULTS
The normal mode of operation is for the analyzer to measure alternately the benzene concentration in one process stream and the toluene concentration in the other process stream. A typical record is shown in Figure 5. The concentration of toluene is about 15%; that of benzene is about 1%. The concentration reproducibility is of the order of 0.15% forztoluene. The analyzer was calibrated using synthetic samples whose composition is given in Table I. The response is linear for both benzene in the range 0 to 5% and toluene in the range 0 to 25%, using peak height measurements.
7% 9 7 5
47.9 63.9 79.8
70 65 60
Xylene
cc.
Iso-octane % cc.
33.3 25.9 18.5
50 50 50
259 241 222
15 15 15
244 244 244 72.9 72.9 72.9
With the GLC column operated a t 101.3" C. and 24.3-p.s.i. carrier gas pressure, the emergence times were 40 seconds for benzene and 73 seconds for toluene. The system was set up to operate on a 20-minute-per-stream cycle. This is the total time to inject a sample, record the peak height, and then backflush the column. Approximately 15 of the 20 minutes were used for backflushing the GLC column. Changes in GLC column temperature a t a concentration of 17.5% toluene increase the peak by approximately 0.570 toluene per 1" C. Changes in carrier gas pressure decrease the peak height approximately 0.5% toluene per 1 p.s.i. for the same conditions. APPLICATIONS
The analyzer was constructed specifically to measure benzene and toluene in the bottoms stream from an aromatics
concentration column. The design can be adapted easily to the analysis of aromatics in different situations. The timing of the programmer can be shifted to select any desired peak. The column temperature can be set to any temperature between 100" and 200" C, In refinery use, the analyzer has proved reliable and required little maintenance. It has been used on several different applications, all requiring the measurements of aromatics in distillation column operations. Because of the chromatographic separation and the selectivity of the ultraviolet detector, no interference problems have arisen in practical applications. LITERATURE CITED
( 1 ) Coulson, D. M., Cavanagh, L. .A., Pittsburgh Conference on Analytical
Chemistry and Applied Spectroscopy, Pittsburgh, Pa., 1961. (2) Gallaway, W. S., Johns, T., Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Pittsburgh, Pa., 1957. (3) Johnstone, R. A. W., Douglas, A. G., Chem. Ind.(London)1959,154. (4) Kaye, Wilbur, ANAL. CHEM.34, 287
(1962). (5) Lutinski, C., Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy,Pittsburgh, Pa., 1957. (6) Penther, C. J., Hickling, J. W., OiZ-Gas J. 59,20, 130 (May 15, 1961). RECEIVEDfor review March 13, 1963. Accepted May 2, 1963. Pittsburgh Conference on Analytical Chemistry and
Applied Spectroscopy, Pittsburgh, Pa., March 1963.
A N e w Analysis of Thermogravimetric Traces HUGH H. HOROWITZ and GERSHON METZGER ESSO Research and Engineering Co. linden, N. 1.
b A new mathematical interpretation of thermogravimetric traces enables one to determine conveniently the kinetic parameters of pyrolysis reactions. The slope of a straight line plot of a function of the weight fraction left vs. the temperature gives the activation energy of pyrolysis. The good agreement between values of activation energy obtained by the new equations and reported literature values for some polymers and hydrated salts serves to validate the new approach. The usefulness of these equations is further demonstrated by their application to two other polymeric systems.
T
analysis (TGA) has come into wide use in the last decade for rapidly assessing the thermal stability of various substances. A number of workers have demonstrated its usefulness (1-3, 6). Often the HERMOQRAVIMETRIC
1464 *
ANALYTICAL CHEMISTRY
pyrolysis occurs through a manystepped mechanism, where the temperature ranges for each step overlap, resulting in irregular weight-temperature curves that may be difficult to analyze. On the other hand, in many cases the trace follows a characteristic path common t o a wide range of decompositions, including many polymer pyrolyses. The sample weight drops slowly as pyrolysis begins, then drops precipitously over a narrow temperature range and finally turns back to a zero slope as the reactant is exhausted. The shape of the curve is determined by the kinetic parameters of the pyrolysis, such as reaction order, frequency factor, and energy of activation. A number of investigators have obtained such information by the analysis of TGA curves (4, 6, 7, 9, 12). Some of the methods described involve either graphic or numerical differentiation of the thermograph, a procedure that is cumbersome, and subject to large errors
when the curves are highly precipitous, as they usually are. I n tn7o instances integral methods were used (4, 12). Doyle (4) integrated the accepted rate equation but found that the resulting expression contained the desired parameters as arguments of transcendental functions. Determination of the parameters required successive approximations or curve fitting. Some years earlier Van Krevelen, Van Heerden, and Huntjens (1.2) described an approximate means of integrating the rate equation, which resulted in a linear plot of the data, from which the energy of activation and pre-exponential factor could easily be extracted. However, in view of the subsequent publications it appears that the value of the development of Van Krevelen et at. was not appreciated. Even those authors used anot.her method, involving the comparison of the data with pre-plotted curves, to analyze their own experimental results. Furthermore, the deter-
mination of the react ion order involved trial plotting of various functions of the sample weight until a linear relation was achieved. It is the purpose of this paper to derive an approximabe integral method similar to, but even simpler than, that of Van Krevelen e1 al., from which pyrolysis rate parameters can easily be extracted, to demonstrate in the derivation that the method is perhaps more widely applicable than might have been originally suspected, to show how in many oases it is possible to determine the reac ;ion order virtually by inspection of the raw data, and to show experimentally that the type of plot proposed does produce straight lines for a number of pyrolyses and that the activation energ.es so derived are in agreement with those obtained by other methods.
reactant and accumulation of products which act as diluent. Thus, expressing concentration on a weight per weight basis : c=-- W W+D where D is the weight of diluents including products. dC=-----dW WdW WdD W+D (W+O)* (W+DY
where
C
= concn., mole fraction
or amount
of reactant IC = specific rate constant 7a = order of reaction t = time and on temperature: k = Ze-&"IRT
(2)
where 2 E* R T
= = = =
frequencyfactor energy of activation gasconstant absolute temperature
Equation 1 should be interpreted to mean that the rate of disappearance of reactant, per unit, volume or per unit total weight or per unit total moles is a power function of the concentration of reactant:
where W is the voiunie, weight, or number of moles of reactant, and W ris the total at any time. This also may be written as:
where dC is a partial derivative referring only to the change in concentration due to the loss of reactant. Where the volume is constant dC may he written as the total derivative dC. In the general case, typical of a pyrolysis, the total change in coricentration is due tjo the decrease of I T as well as the change in total weight due to the loss of
Define 8 such that
(3)
If W , is the initial weight and W{.is the final total weight after pyrolysis, then, since W, grams of reactant yield W{ grams of diluent : dD =
T=T.+e
Then
-w - dW
wo
e
since -
